Lieb-Thirring inequality with semiclassical constant and gradient error term

Abstract

In 1975, Lieb and Thirring derived a semiclassical lower bound on the kinetic energy for fermions, which agrees with the Thomas-Fermi approximation up to a constant factor. Whenever the optimal constant in their bound coincides with the semiclassical one is a long-standing open question. We prove an improved bound with the semiclassical constant and a gradient error term which is of lower order.

6 pages, comments and references added

References in corpus (1)

• Improved Lieb-Oxford exchange-correlation inequality with gradient correction

Cited by in corpus (7)

• The Local Density Approximation in Density Functional Theory
• Universal Functionals in Density Functional Theory
• The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
• Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
• The Validity of the Local Density Approximation for Smooth Short Range Interaction Potentials
• A simple approach to Lieb--Thirring type inequalities
• The Lieb-Thirring inequality for interacting systems in strong-coupling limit